Question

beer Bottles are filled so that they contain an average of 475 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 8 ml.

Answer 1

I attached the rest of your question in the image below.

We use the normal distribution density function f(z) to find the probability of a specific range of values.

Z= ((X-μ)/σ)

μ = 475
σ = 8

a) X< 470 ml

P[X<470] = P[Z<(470-475)/8] = P[Z<(470-475)/8] = P[Z<-0.625] = 0.2659


b) 6 pack with a mean of less than 470ml

Z = ((X-μ)/(σ/√n))

Z = (470-475)/(8/√6)

P [Z<-1.53] = 0.063

c) 12 pack with a mean of less than 470ml

Z = ((X-μ)/(σ/√n))

Z = (470-475)/(8/√12)

P [Z<-2.165] = 0.0152